معکوس‌های تعمیم یافته و تبدیلات دوگال عملگرهای شرطی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده علوم پایه، دانشگاه لرستان، خرم آباد، ایران

2 دانشکده فنی و مهندسی خوی، دانشگاه صنعتی ارومیه، ارومیه، ایران

چکیده

ر این مقاله ابتدا از دیدگاه نظریه اندازه، تبدیل دوگال عملگرهای شرطی از نوع لامبرت را محاسبه می‌کنیم . پس از آن با استفاده از تجزیه قطبی عملگرها، معکوس مور-پنروس $(\widehat{T}^p)$ و معکوس درازین$(\widehat{T}^d)$ این نوع عملگرها را به‌دست می‌آوریم و سپس روابط بین این نوع معکوس‌ها را برای تبدیل دوگال بررسی خواهیم کرد. در انتها با استفاده از مثال‌های متنوع از جمله نمایش ماتریسی درستی نتایج به‌دست آمده را نشان خواهیم داد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Generalized inverses and duggal transformations of conditional operators

نویسندگان [English]

  • Morteza Sohrabi 1
  • Mostafa Hassanlou 2
1 Department of Mathematics, Lorestan University, Khorramabad, Iran
2 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran
چکیده [English]

In this paper, we first calculate the measure theoretic Duggal transform of Lambert conditional operators. Next, by using the polar decomposition of operators, we obtain Moore-Penrose inverse $(\widehat{T}^p)$ and Drazin inverse $(\widehat{T }^d)$ of these types of operators, and then we will check the relationships between these types of inverses for the Duggal transformation. Finally, by using various examples including matrix representation, we will show the correctness of the obtained results.

کلیدواژه‌ها [English]

  • Conditional expectation
  • Moore-Penrose inverse
  • Drazin inverse
  • Duggall transform
  • Lambert operator
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